I think the main aspects putting Copenhagen above Paris in this match-up are the "Tasmania" and "Tropical Zoo" areas: Copenhagen has probably one of the only (if not the only) large Tasmanian-focused exhibit in European zoos, with devils, grey kangaroos, red-necked wallabies and wombats in modern and attractive enclosures. "Tropical Zoo" focuses on worldwide jungles and includes a large butterfly walkthrough, West African crocodiles, and a variety of well-designed enclosures for fish, reptiles, amphibians, and (if I recall correctly) a few larger inverts.
Besides those two exhibits they also have a few enclosures for miscellaneous mammals dotted around the zoo, that all seem adequate for the animals' needs.
Paris is interesting because collection-wise it is perhaps slightly superior (definitely in the reptile department, not sure about the mammals), but a lot of the zoo seems fairly mix-matched... The miscellaneous mammals are somewhat randomly dotted around the zoo in exhibits that don't really highlight them or make them memorable (though seeing quolls in daylight is fairly unique). The reptiles are spread between two reptile houses that have a lot of species, but most of those are in enclosures that seem barely large enough, or enclosures that just aren't very attractive.
My vote definitely goes to Copenhagen here. I thoroughly enjoyed my visits to both zoos, but in this category Copenhagen should definitely win.